Grene was serving as special assistant to the head of the UN stabilization mission in Haiti. He died with 84 other United Nations workers when the UN building in the Haitian capital, Port-au-Prince, collapsed as a result of the magnitude seven quake on January 12.
The 44 year-old political advisor had worked in the destitute Caribbean nation for two years prior to the epic earthquake that took his and the lives of as many as 200,000 people.
Grene, a dual national, was born in Chicago and raised on the family farm in Derrypark, Belturbet, County Cavan from where the funeral cortege made its way to Annagh parish church. Grene was married to County Down native Jennifer. The couple were parents to three children.
Andrew's twin brother, Gregory Grene, is a well known musician in the New York based Celtic Rock group, the Prodigals. The Grene family lives in Hicksville on Long Island. Sons Patrick (21) and Alexander (19) both attend their father's alma mater, the University of Chicago. The youngest child, Rosamund, is 14 years old.
Mourners lined the route to the church as the cortege passed. The coffin was draped in the blue flag of the United Nations. It had been presented to Grene's wife Jennifer, his children, his mother Ethel, his brothers Gregory and Nicholas, and his sister Ruth.
President Mary McAleese was represented at the funeral by her aide-de-camp, Captain Niamh O'Mahoney. Taoiseach Brian Cowen was represented by Commandant Michael Tracey.
A number of politicians, representatives of the Irish defense forces, the Garda Siochana and Irish aid agencies also attended the funeral.
A statement was read out on behalf of the family by Rev. Stephen Clark
It said: "Today words are beggared to tell what is in our hearts. Throughout his life, Andrew gave us unstinting love beyond the bounds of what a sentence or a library could convey. He gave his love to society at large, to his friends and anyone in need of help, and profoundly and deeply to his family and young ones."
Grene's remains were interred in the family plot alongside his father, David Grene, who had been a professor of classics at the University of Chicago. The family has established a foundation in Andrew's name which will be dedicated to the education of Haitian children.